A semi-analytical approach to characterize high-frequency three-dimensional wave propagation through clamp-on flowmeters

Wave propagation analysis at high frequencies is essential for applications involving ultrasound waves, such as clamp-on ultrasonic flowmeters. However, it is extremely challenging to perform a 3D transient analysis of a clamp-on flowmeter using standard tools such as finite element analysis (FEA) due to the enormous associated computational cost. In this study, we separate the clamp-on flowmeter into different domains and analyze them separately. Wave propagation in the fluid domain is analyzed via FEA at low frequencies (100 kHz, 200 kHz, and 500 kHz) and using ray tracing at high frequencies (1 MHz). The behavior in the solid domain (wedges and pipe wall) is analytically characterized via geometric projection. All these individual analyses provide us with different scaling factors with which the waves in the respective domains scale when 3D effects are considered. The complete clamp-on system is then analyzed in 2D via the Discontinuous Galerkin (DG) method to obtain the response at the receiver. The receiving signal is then scaled using the aforementioned scaling factors to accurately capture the wave propagation behavior of the clamp-on system in 3D. The output signal from the 2D analysis then becomes much clearer so that the fluid signal can be identified straightforwardly, which would be nearly impossible otherwise.